Existence of static vacuum extensions for Bartnik boundary data near Schwarzschild spheres

TL;DR

This paper proves the existence and local uniqueness of static vacuum extensions for Bartnik boundary data close to Schwarzschild spheres, advancing understanding of geometric boundary problems in general relativity.

Contribution

It establishes new existence and uniqueness results for static vacuum extensions near Schwarzschild boundary data, a previously unresolved problem.

Findings

Existence of static vacuum extensions near Schwarzschild data

Local uniqueness of these extensions

Advancement in geometric boundary problem understanding

Abstract

We obtain existence and local uniqueness of asymptotically flat, static vacuum extensions for Bartnik data on a sphere near the data of a sphere of symmetry in a Schwarzschild manifold.